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The equations of classical mechanics can be used to model the time evolution of countless physical systems, from the astrophysical to the atomic scale. Accurate numerical integration requires small time steps, which limits the computational…

How can we effectively encode evolving information over dynamic graphs into low-dimensional representations? In this paper, we propose DyRep, an inductive deep representation learning framework that learns a set of functions to efficiently…

Predicting high-dimensional dynamical systems with irregular time steps presents significant challenges for current data-driven algorithms. These irregularities arise from missing data, sparse observations, or adaptive computational…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

Understanding the dynamical processes that govern the performance of functional materials is essential for the design of next generation materials to tackle global energy and environmental challenges. Many of these processes involve the…

Machine learning techniques including neural networks are popular tools for materials and chemical scientists with applications that may provide viable alternative methods in the analysis of structure and energetics of systems ranging from…

Reduced-order models are central to motion planning and control of quadruped robots, yet existing templates are often hand-crafted for a specific locomotion modality. This motivates the need for automatic methods that extract task-specific,…

The accurate simulation of complex dynamics in fluid flows demands a substantial number of degrees of freedom, i.e. a high-dimensional state space. Nevertheless, the swift attenuation of small-scale perturbations due to viscous diffusion…

With the growing size and complexity of turbulent flow models, data compression approaches are of the utmost importance to analyze, visualize, or restart the simulations. Recently, in-situ autoencoder-based compression approaches have been…

We introduce a novel self-supervised learning framework that automatically learns representations from input computer-aided design (CAD) models for downstream tasks, including part classification, modeling segmentation, and machining…

We present a data-driven pipeline for model building that combines interpretable machine learning, hydrodynamic theories, and microscopic models. The goal is to uncover the underlying processes governing nonlinear dynamics experiments. We…

Intelligent biological systems are characterized by their embodiment in a complex environment and the intimate interplay between their nervous systems and the nonlinear mechanical properties of their bodies. This coordination, in which the…

Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a geometrically consistent way of treating complex domains,…

Accurate and efficient physical simulations are essential in science and engineering, yet traditional numerical solvers face significant challenges in computational cost when handling simulations across dynamic scenarios involving complex…

While variational autoencoders have been successful in several tasks, the use of conventional priors are limited in their ability to encode the underlying structure of input data. We introduce an Encoded Prior Sliced Wasserstein AutoEncoder…

Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…

Molecular property calculations are the bedrock of chemical physics. High-fidelity \textit{ab initio} modeling techniques for computing the molecular properties can be prohibitively expensive, and motivate the development of…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

Classical autoencoders are neural networks that can learn efficient low dimensional representations of data in higher dimensional space. The task of an autoencoder is, given an input $x$, is to map $x$ to a lower dimensional point $y$ such…

The vast majority of systems of practical interest are characterised by nonlinear dynamics. This renders the control and optimization of such systems a complex task due to their nonlinear behaviour. Additionally, standard methods such as…